The visitors struggled to find their rhythm in the early stages of the encounter, surviving from a number of chances until Oleg Kuzmin found the back of the net.
After conceding, the Championship outfit failed to net an equaliser before the half-time interval, requiring manager Owen Coyle to make some changes in the second 45 minutes.
The Scotsman did so by introducing Nick Powell from the bench, which improved Wigan's performance in the second half, but they still struggled to force through a dangerous attack.
The visitors' closest effort came when Roger Espinoza moved into the area and took a shot towards goal, but his chance was blocked by Kazan's defence.
The Latics came at Rubin again through Powell, who drilled past three Rubin shirts before unleashing a left-footed shot towards the net, but his effort flew above the top corner.
Wigan continued to press and they came agonisingly close to equalising through Thomas Rogne, who latched on to a lofting pass from Espinoza in the box, but his headed effort bounced off the post to the bar and away from the net.